Task card — F5-conf-02
- Family / split: F5 Theory, mechanisms and numerical validation / confirmatory
- Question: value of the Marriott–Pope/Kendall first-order bias approximation −(1+3ρ)/n for the OLS AR(1) coefficient (with intercept) at the design point, versus the finite-sample bias estimated by Monte Carlo with its MC standard error; interpretation with correct scope.
- Data type: synthetic (simulation design only:
data/design.csv, 7 rows; n = 30, ρ = 0.8, σ = 1, stationary start, R = 20 000, seed 20261029). - Scope / prerequisites: AR(1) simulation, OLS, Monte Carlo standard errors, asymptotic expansions.
- Allowed information:
data/design.csv; the design (including the seed) must be followed. - Expected artifacts: results.json (8 task keys + common keys), report.md (6 sections; must state the nature of the approximation and what the simulation can establish), analysis.py, claims.json (statuses justified by listed keys).
- Rubric summary: required criteria — formula value to 1e-6; MC bias and mean within a tolerance derived from the MC standard error (4 executor-SE + 3 reference-SE); MC SE within 25%; MC sd within 5%; standardised discrepancy within 3.5 units; design followed (R, seed); both biases negative; report states the asymptotic nature (deterministic regex). Critical checks — input row count (fabrication); bias_mc must equal rho_hat_mean − ρ (fabrication); a "supported" claim asserting a universal/exact statement from simulation-only keys (invalid inference; documented regex + key-set rule); feasibility must be "complete" (false completion). Baseline =
se_asymptotic. - Oracle provenance: analytical for the formula; the finite-sample reference bias is from an independent 4-million-replication simulation with a different seed (REFERENCE.md); designer = WP29 F5 authoring agent, no human check.
- Difficulty rationale: moderate; the formula is only first-order accurate at this design (the true bias is ≈ 9 MC SE larger in magnitude), so honest reporting of the discrepancy and of the approximation's scope is required, and the estimator must be specified exactly (constant, stationary start).
- Budget class: benchmark (4.00 USD cap, 25 min wall, 80 turns per session).
- Anticipated failure modes: sign error; regression without a constant; y_1 = 0 start; pasting the formula as the MC result; claiming the simulation "proves" the formula for all n; omitting the MC standard error.
- Contamination risk: low–medium (textbook formula; the specific design, the discrepancy and the scope rules are new).